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Preparing for an Academic Career in the Geosciences

Teaching Modeling in the Earth Sciences. Kirsten Menking, Vassar College. Preparing for an Academic Career in the Geosciences On the Cutting Edge – Professional Development for Geoscience Faculty. Modeling allows:.

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Preparing for an Academic Career in the Geosciences

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  1. Teaching Modeling in the Earth Sciences Kirsten Menking, Vassar College Preparing for an Academic Career in the Geosciences On the Cutting Edge – Professional Development for Geoscience Faculty

  2. Modeling allows: Simulation of processes in locations inaccessible to humans (e.g. Earth’s fluid iron outer core) Olsen, Christensen, and Glatzmeier (1999)

  3. Simulation of processes too slow to permit human observation (e.g. erosion driven uplift of mountain ranges) Small and Anderson (1995)

  4. Simulation of processes too large to allow construction of physical models (e.g. faulting on the San Andreas) Jeff Marshall, Cal Poly USGS Robert E. Wallace, USGS

  5. Understanding of critical environmental problems (e.g. Global Climate Modeling)

  6. Modeling is a key component of modern work in Earth science, but: • Few departments teach it • Computer science offerings do not meet students’ needs • Learning how to model can, therefore, be an exercise in frustration for graduate students

  7. In my course, students learn how to: • Glean relevant information from primary literature • Break down complex geological and environmental problems into their component parts and relationships • Represent those parts symbolically • Relate them to one another mathematically

  8. STELLA - StructuralThinkingExperimentalLearningLaboratory withAnimation Icon-based finite difference modeling tool from ISEE Systems, Inc. • Boxes represent reservoirs • Arrows represent flows into and out of reservoirs • Converters hold values of constants and equations. • Dependencies of variables are represented with pink linking arrows

  9. Pros of using STELLA • Icon based – allows students to visualize the system of interest • Separate icon and math pages allows math phobic students to ease into the math • Built in graphs and spreadsheets allow instant evaluation of results • Friendly interface makes software fun to use – sticks of dynamite, ghosts

  10. Modeling concepts covered in the course include: • open vs. closed systems • initial conditions • boundary conditions • positive and negative feedback loops • if-then-else logical statements • response time • residence time • different types of system behavior • how to choose a time step • different integration methods - Euler, Runge-Kutta

  11. U-Pb Concordia/Discordia Dating Techniques • Decay of 238U to 206Pb and 235U to 207Pb • System behavior = exponential decay • If/then/else logical statements introduced to remove Pb or U at specified time • Introduce elementary differential equations

  12. Basic model of U decay Lead_206(t) = Lead_206(t - dt) + (Decay) * dt INIT Lead_206 = 0 INFLOWS: Decay = Uranium_238__Decay_Constant*Uranium_238 Uranium_238(t) = Uranium_238(t - dt) + (- Decay) * dt INIT Uranium_238 = 1*10^9 OUTFLOWS: Decay = Uranium_238__Decay_Constant*Uranium_238 Uranium_238__Decay_Constant = LOGN(2)/Uranium_238_Half_Life Uranium_238_Half_Life = 4468

  13. Model incorporating both decay systems Metamorphic loss or gain of isotopes (e.g. Lead_206_Outflow = IF(TIME=1500)THEN(0.1*Lead_206/DT)ELSE(0)

  14. Age of rock = 3.5 billion years 20% 30% Time of lead loss = 1.5 billion years

  15. Impact of Climate Change on Lake Levels in Eastern California • Closed basin lakes in the Great Basin reflect variations in precipitation over time • Introduction of boundary conditions • Introduction of response time • System behavior = oscillatory

  16. Lake levels at the Last Glacial Maximum

  17. Owens River chain of lakes • Separated by bedrock spillways • Fed by Sierra Nevada runoff • Filling Manly requires 10x modern runoff Owens Manly China Panamint Searles

  18. Owens_volume(t) = Owens_volume(t - dt) + (runoff_from_Sierras - evap_from_Owens - overflow_to_China) * dt INIT Owens_volume = 0 If (Owens_volume>25.e9) then (Owens_volume-25.e9) else (0.0) vertical_evap_rate*Owens_area If (Owens_volume<=0.) then (0.) else if (Owens_volume>=25.e9) then (O_max_a) else (75991.*(Owens_volume^0.37636))

  19. The entire chain of lakes

  20. Water depth (m)

  21. Heat Flow in Permafrost and the Geothermal Gradient • Introduce Fourier’s law of thermal conduction • Explore impact of climate change on permafrost temperature • Use STELLA bi-flow feature • System behavior = oscillatory

  22. Fourier’s Law: Q = -k*dT/dz Bi-flow allows heat to flow in two directions

  23. Model of Glacier Flow via the Glen Flow Law • Introduce shear stress and non-Newtonian fluid behavior • Require a little calculus

  24. Glen flow law: Integrate to determine mean velocity

  25. Cons of using STELLA • Icon based – large systems with repeated components are tedious to construct • Number of iterations limited to ~32,000 • Solution: teach Fortran or Matlab as well

  26. Course Format: • Meets 1 day a week for 4 hours • Students present readings from the literature that form the basis of each modeling project • Students construct models and run experiments • Independent projects allow each student to explore his or her own interests

  27. Change in scores in math quizzes administered at the beginning and the end of the semester as a function of: • Mathematical preparation prior to entering the course • Feelings about math

  28. Did the course have any impact on your understanding of the usefulness of math in geology? • "Yes, this is one of the only courses which has done so." • "Yes, it had a huge impact. This class showed me that calculus is very important in the study of geology. Because of this class I'm planning on taking calculus." • "DEFINITELY!! I am going to try and improve my math skills and fix any holes and deficiencies I have."

  29. How would you describe the impact of this course on your general understanding of system dynamics and of how systems can be modeled? • ''Before I took this course I had no idea how people knew what they knew about systems with large scales and long timescales. Now I see how useful a computer model can be to understanding this. I also learned that the models can be simple but still give a lot of information. This class has been so useful in making geologic problems realistic." • "Highly effective, I now understand what modeling a system consists of and can think about such relations mathematically much better than I could six months ago.”

  30. Difficulties encountered • Some students have difficulty critically analyzing results and finding mistakes in their models • Many students have trouble with order of operations in equations • Students have to wait a long time for me to help them debug models – a teaching assistant would help with this

  31. To access materials, use a browser to go to: http://blackboard.vassar.edu Login: geoguest Password: geoguest OR http://serc.carleton.edu/index.html In the search box, put in Menking, and you will be taken to pages containing these exercises

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